C₂×D₉₂₇₅ #49150667

order	37100
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₈₅₅₀
direct product	C₂×D₉₂₇₅
unambiguous semidirect product	(C₂×C₇)⋊D₁₃₂₅
unambiguous semidirect product	(C₂×C₂₅)⋊D₃₇₁
unambiguous semidirect product	(C₂×C₅₃)⋊D₁₇₅

Splittings

Fitting	C₂×C₇×C₂₅×C₅₃ ⋊ C₂
derived, Hall	C₇×C₂₅×C₅₃ ⋊ C₂²
Hall	C₂₅×C₅₃ ⋊ C₂×D₇
Hall	C₇×C₅₃ ⋊ C₂×D₂₅
Hall	C₇×C₂₅ ⋊ C₂×D₅₃
Sylow	C₅₃ ⋊ C₂×D₁₇₅
Sylow	C₂₅ ⋊ C₂×D₃₇₁
Sylow	C₇ ⋊ C₂×D₁₃₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₂₇₅
commutator, cosocle, hypocenter	C₇×C₂₅×C₅₃	C₂²
Frattini	C₅	C₂×D₁₈₅₅
Fitting	C₂×C₇×C₂₅×C₅₃	C₂
socle	C₂×C₅×C₇×C₅₃	D₅
LCS	G ▷ C₇×C₂₅×C₅₃
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 18550

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

Conjugacy classes & character table

9278 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37100, 29);

C2×D9275 #49150667