Finite Group Databasebeta

C8×#13063253 #24987305

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC8×#13063253

Splittings

FittingC42×C8×C43 ⋊ C2
SylowC43 ⋊ C8×#104

Subgroups

subgroupG/H
centerC4×C8D172
commutatorC4×C43C2×C4×C8
FrattiniC2×C42C22×D43
FittingC42×C8×C43C2
socleC22×C43C4×C22⋊C4
prime radicalC2×#10621898C2×C4
cosocleC2×C42×C43C23
hypercenterC42×C8D43
hypocenterC43C8×#104
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4×C8 ◁ C2×C4×C8 ◁ C42×C8

554 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 60276);