C₃₇×C₁₃⋊D₁₃ #27159776

order	12506
isoclinism	isoclinic class of C₁₃⋊D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₇ · Schur multiplier (H₂) = C₁₃

Aliases

direct product	C₃₇×C₁₃⋊D₁₃
unambiguous semidirect product	C₁₃⋊(D₁₃×C₃₇)

Splittings

Fitting, socle, Hall	C₁₃²×C₃₇ ⋊ C₂
derived, Sylow	C₁₃² ⋊ C₂×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃₇	C₁₃⋊D₁₃
commutator, cosocle, hypocenter	C₁₃²	C₂×C₃₇
Frattini	C₁	G
Fitting, socle	C₁₃²×C₃₇	C₂
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₃₇

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 6253

A minimal faithful permutation representation — 3 generators on 63 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(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);(14,15,17,19,21,23,25,26,24,22,20,18,16);(1,2,4,6,8,10,12,13,11,9,7,5,3)

Conjugacy classes & character table

3182 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₃²×C₃₇, (C₁₃⋊D₁₃)⋊D₃₇, D₃₇×C₁₃⋊D₁₃, …
maximal normal subgroup of	D₁₃²×C₃₇, (C₁₃⋊D₁₃)⋊D₃₇, D₃₇×C₁₃⋊D₁₃, …
maximal quotient of	C₃₇×#10621725, C₂×C₃₇×C₁₃⋊D₁₃, C₃×C₃₇×C₁₃⋊D₁₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12506, 7);

C37×C13⋊D13 #27159776