Finite Group Databasebeta

C2×#22561642 #30884656

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22561642

Splittings

SylowC67 ⋊ C2×#2077

Subgroups

subgroupG/H
centerC24C2×D268
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC22×C22⋊C8×C67C2
socleC24×C67C2×D4
prime radicalC25×C67D4
hypercenterC22×C22⋊C8D67
hypocenterC67C2×#2077
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

1270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2704 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 198393);