Finite Group Databasebeta

C2×#22558095 #30745951

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#22558095

Splittings

SylowC67 ⋊ C2×#1297

Subgroups

subgroupG/H
centerC22×C4(C2×D67)⋊C4
commutatorC2×C4×C67C2×C42
FrattiniC23×C4C22×D67
FittingC2×C4×C22⋊C4×C67C2
socleC23×C67#95
prime radicalC25×C67D4
cosocleC23×C4×C67C23
hypercenterC2×C4×C22⋊C4D67
hypocenterC67C2×#1297
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 59688);