C₂×D₆₄₇₅ #39905959

order	25900
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₂₉₅₀
direct product	C₂×D₆₄₇₅
unambiguous semidirect product	(C₂×C₇)⋊D₉₂₅
unambiguous semidirect product	(C₂×C₂₅)⋊D₂₅₉
unambiguous semidirect product	(C₂×C₃₇)⋊D₁₇₅

Splittings

Fitting	C₂×C₇×C₂₅×C₃₇ ⋊ C₂
derived, Hall	C₇×C₂₅×C₃₇ ⋊ C₂²
Hall	C₂₅×C₃₇ ⋊ C₂×D₇
Hall	C₇×C₃₇ ⋊ C₂×D₂₅
Hall	C₇×C₂₅ ⋊ C₂×D₃₇
Sylow	C₃₇ ⋊ C₂×D₁₇₅
Sylow	C₂₅ ⋊ C₂×D₂₅₉
Sylow	C₇ ⋊ C₂×D₉₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₆₄₇₅
commutator, cosocle, hypocenter	C₇×C₂₅×C₃₇	C₂²
Frattini	C₅	C₂×D₁₂₉₅
Fitting	C₂×C₇×C₂₅×C₃₇	C₂
socle	C₂×C₅×C₇×C₃₇	D₅
LCS	G ▷ C₇×C₂₅×C₃₇
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 12950

A minimal faithful permutation representation — 2 generators on 71 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);(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)(36,71)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,64)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58)(50,57)(51,56)(52,55)(53,54)

Conjugacy classes & character table

6478 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₅₉₀₀
maximal normal subgroup of	D₂₅₉₀₀
maximal quotient of	Dic₁₂₉₅₀, D₂₅₉₀₀

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25900, 29);

C2×D6475 #39905959