Finite Group Databasebeta

Q32×Dic127 #30640589

order16256
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productQ32×Dic127

Splittings

SylowC127 ⋊ C4×Q32

Subgroups

subgroupG/H
centerC22D8×D127
commutatorC8×C127C22×C4
FrattiniC2×C8C22×D127
FittingC2×Q32×C127C2
socle, prime radicalC22×C127C2×D8
cosocleC2×C8×C127C23
hypercenterC2×Q32D127
hypocenterC127C4×Q32
LCSG ▷ C8×C127 ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

150 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 6369);