Finite Group Databasebeta

#22597241

order9088
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

FittingC2×#131×C71 ⋊ C2
SylowC71 ⋊ #2955

Subgroups

subgroupG/H
centerC8C2×C22⋊D71
commutatorC4×C71C23×C4
FrattiniC2×C4C23×D71
FittingC2×#131×C71C2
socleC2×C71C2×C4×D4
hypercenterC2×#131D71
hypocenterC71#2955
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C8 ◁ C22×C8 ◁ C2×#131

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,71|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^b=h^70

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#31914319, #31914320, #31914322, …
maximal normal subgroup of#31914319, #31914320, #31914322, …
maximal quotient ofC8×#14556153, C8×#14556154, C8×#14556158, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9088, 13411);