Finite Group Databasebeta

C2×#22569930 #31723227

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22569930

Splittings

FittingC22×#108×C67 ⋊ C2
SylowC67 ⋊ C2×#3067

Subgroups

subgroupG/H
centerC2×C4#14524018
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC22×#108×C67C2
socleC22×C67C2×#121
hypercenterC22×#108D67
hypocenterC67C2×#3067
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#108

2650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1036964);