Finite Group Databasebeta

#25002860

order11008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4

Aliases

No aliases for this group.

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ #10925

Subgroups

subgroupG/H
centerC24C2×D172
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC22×C4×C8×C43C2
socleC24×C43C2×D4
prime radicalC23×D172C22
cosocleC23×C4×C43C23
hypercenterC22×C4×C8D43
hypocenterC43#10925
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×C8

1334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=f,b^2=g,c^2=ef,d^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^42

Conjugacy classes & character table

2776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 75831);