Finite Group Databasebeta

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#44449685

order	29824
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

C₂₃₃ ⋊ #1292

Subgroups

	subgroup	G/H
center	C₂²	#21418442
commutator	C₂×C₄×C₂₃₃	C₄²
Frattini	C₂×C₄²	C₂×D₂₃₃
Fitting	C₂×C₄⋊C₈×C₂₃₃	C₂
socle	C₂²×C₂₃₃	#95
prime radical	C₂³×C₂₃₃	C₄⋊C₄
cosocle	C₂×C₄²×C₂₃₃	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₃₃
hypocenter	C₂₃₃	#1292
LCS	G ▷ C₂×C₄×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 14912

Polycyclic presentation:

2^7,233|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^232,d^b=dg

Conjugacy classes & character table

4672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29824, 2385);