Finite Group Databasebeta

C2×#22561510 #30883708

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

Aliases

direct productC2×#22561510

Splittings

FittingC22×#108×C67 ⋊ C2
SylowC67 ⋊ C2×#2052

Subgroups

subgroupG/H
centerC23#14524018
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC22×#108×C67C2
socleC23×C67#121
prime radicalC22×#11761628C22
hypercenterC22×#108D67
hypocenterC67C2×#2052
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#108

1362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 197445);