Finite Group Databasebeta

C8×#13063252 #24987303

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

Aliases

direct productC8×#13063252

Splittings

SylowC43 ⋊ C8×#104

Subgroups

subgroupG/H
centerC4×C8C22⋊D43
commutatorC4×C43C2×C4×C8
FrattiniC2×C42C22×D43
FittingC8×#41×C43C2
socleC22×C43C4×C22⋊C4
prime radicalC2×#41×C43C2×C4
cosocleC2×C42×C43C23
hypercenterC8×#41D43
hypocenterC43C8×#104
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4×C8 ◁ C2×C4×C8 ◁ C8×#41

554 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 60274);