Finite Group Databasebeta

C2×#22573787 #31762901

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

Aliases

direct productC2×#22573787

Splittings

FittingC2×#533×C67 ⋊ C2
SylowC67 ⋊ C2×Q8×#41

Subgroups

subgroupG/H
centerC22×C4C23×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#533×C67C2
socleC23×C67C25
prime radicalC22×#11761628C22
hypercenterC2×#533D67
hypocenterC67C2×Q8×#41
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×#533

7522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1948 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1076638);