Finite Group Databasebeta

C2×#22562489 #31011315

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#22562489

Splittings

SylowC67 ⋊ C2×#2254

Subgroups

subgroupG/H
centerC23C2×#11761613
commutator, cosocleC2×C8×C67C24
FrattiniC2×C8C23×D67
FittingC2×#500×C67C2
socle, prime radicalC23×C67C2×D8
hypercenterC2×#500D67
hypocenterC67C2×#2254
LCSG ▷ C2×C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#500

558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

1528 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 325052);