Finite Group Databasebeta

C2×#30654270 #45656196

order32576
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#30654270

Splittings

SylowC509 ⋊ C2×#97

Subgroups

subgroupG/H
centerC23C2×#14523266
commutatorC2×C509C2×C42
FrattiniC22C22×#14523266
FittingC22×C4×C509C4
socle, prime radicalC23×C509C2×C4
cosocleC2×Dic509C23
hypercenterC22×C4#14523266
hypocenterC509C2×#97
LCSG ▷ C2×C509 ▷ C509
UCSC1 ◁ C23 ◁ C22×C4

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32576

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32576, 1507);