C₂×C₇×C₃⋊(C₁₇⋊D₁₇) #37566308

order	24276
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂×C₁₇

Aliases

direct product	C₂×C₇×C₃⋊(C₁₇⋊D₁₇)
unambiguous semidirect product	(C₂×C₃)⋊(C₇×C₁₇⋊D₁₇)
unambiguous semidirect product	(C₂×C₁₇)⋊(C₇×D₅₁)

Splittings

Fitting, socle	C₂×C₃×C₇×C₁₇² ⋊ C₂
derived, Hall	C₃×C₁₇² ⋊ C₂²×C₇
Hall	C₃×C₇×C₁₇² ⋊ C₂²
Hall	C₇×C₁₇² ⋊ C₂×D₃
Sylow	C₁₇² ⋊ C₂×D₃×C₇
Hall	C₃×C₇ ⋊ C₂×C₁₇⋊D₁₇
Sylow	C₃ ⋊ C₂×C₇×C₁₇⋊D₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇	C₃⋊(C₁₇⋊D₁₇)
commutator, cosocle, hypocenter	C₃×C₁₇²	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₇²	C₂
LCS	G ▷ C₃×C₁₇²
UCS	C₁ ◁ C₂×C₇

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 12138

A minimal faithful permutation representation — 3 generators on 46 points:

(2,3)(4,5,6,7,8,9,10)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44);(1,2,3)(28,29,31,33,35,37,39,41,43,44,42,40,38,36,34,32,30)(45,46);(11,12,14,16,18,20,22,24,26,27,25,23,21,19,17,15,13)

Conjugacy classes & character table

6090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24276, 161);

C2×C7×C3⋊(C17⋊D17) #37566308