Finite Group Databasebeta

C2×#22569077 #31719977

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22569077

Splittings

SylowC67 ⋊ C2×#2950

Subgroups

subgroupG/H
centerC23C2×D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC23×Q16×C67C2
socleC23×C67C22×D4
prime radicalC24×C67C2×D4
cosocleC2×C4×C67C25
hypercenterC23×Q16D67
hypocenterC67C2×#2950
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

2654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1936 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033714);