Finite Group Databasebeta

C2×#22551680 #30657814

order16448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22551680

Splittings

SylowC257 ⋊ C2×#131

Subgroups

subgroupG/H
centerC22C22×#11759967
commutatorC2×C257C23×C4
FrattiniC2C23×#11759967
FittingC2×Q8×C257C4
socleC22×C257C22×C4
prime radicalC2×#16861619C2
cosocleDic257C24
hypercenterC2×Q8#11759967
hypocenterC257C2×#131
LCSG ▷ C2×C257 ▷ C257
UCSC1 ◁ C22 ◁ C2×Q8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8224

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 1626);