Finite Group Databasebeta

C2×#22574033 #31764308

order17152
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#22574033

Splittings

FittingC22×#125×C67 ⋊ C2
SylowC67 ⋊ C2×#3504

Subgroups

subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC22×#125×C67C2
socleC23×C67C25
prime radicalC22×#11761628C22
hypercenterC22×#125D67
hypocenterC67C2×#3504
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×#125

6958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1936 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1078045);