Finite Group Databasebeta

C2×#22560461 #30856758

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22560461

Splittings

SylowC67 ⋊ C2×#1863

Subgroups

subgroupG/H
centerC24D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC22×#103×C67C2
socle, prime radicalC24×C67C2×D4
cosocleC22×C4×C67C24
hypercenterC22×#103D67
hypocenterC67C2×#1863
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

1542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

1924 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 170495);