Finite Group Databasebeta

C2×Q8×C22⋊D127 #30652202

order16256
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×Q8×C22⋊D127

Splittings

FittingC23×Q8×C127 ⋊ C2
SylowC127 ⋊ C2×D4×Q8

Subgroups

subgroupG/H
centerC23C23×D127
commutator, cosocleC22×C127C25
FrattiniC22C24×D127
FittingC23×Q8×C127C2
socleC23×C127C24
prime radicalC22×C22⋊D127C22
hypercenterC23×Q8D127
hypocenterC127C2×D4×Q8
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C23 ◁ C23×Q8

1568 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 17982);