Finite Group Databasebeta

C22×Q8×Dic127 #30651906

order16256
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×Q8×Dic127

Splittings

SylowC127 ⋊ C22×C4×Q8

Subgroups

subgroupG/H
centerC24C22×D127
commutatorC2×C127C24×C4
FrattiniC22C24×D127
FittingC23×Q8×C127C2
socle, prime radicalC24×C127C23
cosocleC22×C127C25
hypercenterC23×Q8D127
hypocenterC127C22×C4×Q8
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C24 ◁ C23×Q8

1664 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 17686);