Finite Group Databasebeta

C2×#19132551 #25006297

order11008
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19132551

Splittings

FittingC2×C4×C16×C43 ⋊ C2
SylowC43 ⋊ C2×D4⋊C16

Subgroups

subgroupG/H
centerC22×C8D172
commutatorC4×C43C22×C16
FrattiniC4×C8C22×D43
FittingC2×C4×C16×C43C2
socleC23×C43C22⋊C8
prime radicalC22×D172C8
cosocleC4×C8×C43C23
hypercenterC2×C4×C16D43
hypocenterC43C2×D4⋊C16
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C4×C16

470 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, 79268);