C₂×D₇₅₉₅ #44477121

order	30380
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₅₁₉₀
direct product	C₂×D₇₅₉₅
unambiguous semidirect product	(C₂×C₅)⋊D₁₅₁₉
unambiguous semidirect product	(C₂×C₃₁)⋊D₂₄₅
unambiguous semidirect product	(C₂×C₄₉)⋊D₁₅₅

Splittings

Fitting	C₂×C₅×C₃₁×C₄₉ ⋊ C₂
derived, Hall	C₅×C₃₁×C₄₉ ⋊ C₂²
Hall	C₃₁×C₄₉ ⋊ C₂×D₅
Hall	C₅×C₄₉ ⋊ C₂×D₃₁
Hall	C₅×C₃₁ ⋊ C₂×D₄₉
Sylow	C₄₉ ⋊ C₂×D₁₅₅
Sylow	C₃₁ ⋊ C₂×D₂₄₅
Sylow	C₅ ⋊ C₂×D₁₅₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₇₅₉₅
commutator, cosocle, hypocenter	C₅×C₃₁×C₄₉	C₂²
Frattini	C₇	C₂×D₁₀₈₅
Fitting	C₂×C₅×C₃₁×C₄₉	C₂
socle	C₂×C₅×C₇×C₃₁	D₇
LCS	G ▷ C₅×C₃₁×C₄₉
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 15190

A minimal faithful permutation representation — 2 generators on 87 points:

(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(4,7)(5,6)(9,56)(10,55)(11,54)(12,53)(13,52)(14,51)(15,50)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)(58,87)(59,86)(60,85)(61,84)(62,83)(63,82)(64,81)(65,80)(66,79)(67,78)(68,77)(69,76)(70,75)(71,74)(72,73)

Conjugacy classes & character table

7598 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃₀₃₈₀
maximal normal subgroup of	D₃₀₃₈₀
maximal quotient of	Dic₁₅₁₉₀, D₃₀₃₈₀

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 30);

C2×D7595 #44477121