Finite Group Databasebeta

← Prev (#38740586) Next (#38740588) →

#38740587

order	25216
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

C₁₉₇ ⋊ #1292

Subgroups

	subgroup	G/H
center	C₂²	#20263233
commutator	C₂×C₄×C₁₉₇	C₄²
Frattini	C₂×C₄²	C₂×D₁₉₇
Fitting	C₂×C₄⋊C₈×C₁₉₇	C₂
socle	C₂²×C₁₉₇	#95
prime radical	C₂³×C₁₉₇	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉₇	C₂²
hypercenter	C₂×C₄⋊C₈	D₁₉₇
hypocenter	C₁₉₇	#1292
LCS	G ▷ C₂×C₄×C₁₉₇ ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12608

Polycyclic presentation:

2^7,197|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^196,d^b=dg

Conjugacy classes & character table

3952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 2385);