Finite Group Databasebeta

C2×#19132722 #25011576

order11008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19132722

Splittings

SylowC43 ⋊ C2×#1394

Subgroups

subgroupG/H
centerC23#13063240
commutatorC2×C4×C43C2×C42
FrattiniC22×Q8C22×D43
FittingC2×C43×#391C2
socleC23×C43#99
prime radicalC24×C43C22⋊C4
cosocleC22×Q8×C43C23
hypercenterC2×#391D43
hypocenterC43C2×#1394
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24 ◁ C23×Q8 ◁ C2×#391

818 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 84547);