Finite Group Databasebeta

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#44505320

order	30848
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

C₂₄₁ ⋊ #1292

Subgroups

	subgroup	G/H
center	C₂²	#21440549
commutator	C₂×C₄×C₂₄₁	C₄²
Frattini	C₂×C₄²	C₂×D₂₄₁
Fitting	C₂×C₄⋊C₈×C₂₄₁	C₂
socle	C₂²×C₂₄₁	#95
prime radical	C₂³×C₂₄₁	C₄⋊C₄
cosocle	C₂×C₄²×C₂₄₁	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₄₁
hypocenter	C₂₄₁	#1292
LCS	G ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15424

Polycyclic presentation:

2^7,241|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^240,d^b=dg

Conjugacy classes & character table

4832 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 2385);