Finite Group Databasebeta

C2×#22560766 #30857873

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#22560766

Splittings

SylowC67 ⋊ C2×#1916

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutatorC22×C67C23×C8
FrattiniC22×C4C23×D67
FittingC22×C4×C8×C67C2
socle, prime radicalC24×C67C22×C4
cosocleC22×C4×C67C24
hypercenterC22×C4×C8D67
hypocenterC67C2×#1916
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C22×C4×C8

1134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

4336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 171610);