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#46780631

order	33664
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

C₂₆₃ ⋊ #1296

Subgroups

	subgroup	G/H
center	C₂³	(C₂×D₂₆₃)⋊C₄
commutator	C₂×C₄×C₂₆₃	C₄²
Frattini	C₂×C₄²	C₂×D₂₆₃
Fitting	C₂×C₄⋊C₈×C₂₆₃	C₂
socle, prime radical	C₂³×C₂₆₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₂₆₃	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₆₃
hypocenter	C₂₆₃	#1296
LCS	G ▷ C₂×C₄×C₂₆₃ ▷ C₂²×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 33664

Polycyclic presentation:

2^7,263|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^262,c^b=cg

Conjugacy classes & character table

5278 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33664, 2394);