Finite Group Databasebeta

C2×#22568906 #31719688

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

Aliases

direct productC2×#22568906

Splittings

FittingC2×#408×C67 ⋊ C2
SylowC67 ⋊ C2×#2929

Subgroups

subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×#408×C67C2
socleC23×C67C23×C4
prime radicalC2×#16863903C2
cosocleC2×C4×C67C25
hypercenterC2×#408D67
hypocenterC67C2×#2929
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×#408

3046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033425);