Finite Group Databasebeta

C2×#22551646 #30657694

order16448
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#22551646

Splittings

FittingC2×C8×C257 ⋊ C4
SylowC257 ⋊ C2×#97

Subgroups

subgroupG/H
centerC2×C4C2×#11759967
commutatorC2×C257C2×C42
FrattiniC4C22×#11759967
FittingC2×C8×C257C4
socleC22×C257C42
prime radicalC22×D257C2×C4
cosocleC4×D257C23
hypercenterC2×C8#11759967
hypocenterC257C2×#97
LCSG ▷ C2×C257 ▷ C257
UCSC1 ◁ C2×C4 ◁ C2×C8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4112

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 1506);