Finite Group Databasebeta

C4×#16861257 #30651942

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

Aliases

direct productC4×#16861257

Splittings

FittingC2×C4×Q8×C127 ⋊ C2
SylowC127 ⋊ C4×2−1+4

Subgroups

subgroupG/H
centerC2×C4C23×D127
commutatorC2×C127C24×C4
FrattiniC22C24×D127
FittingC2×C4×Q8×C127C2
socle, cosocleC22×C127C25
prime radicalC2×#16861257C2
hypercenterC2×C4×Q8D127
hypocenterC127C4×2−1+4
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

1492 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 17722);