Finite Group Databasebeta

C2×#22561081 #30859662

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#22561081

Splittings

SylowC67 ⋊ C2×#1971

Subgroups

subgroupG/H
centerC24D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC23×Q16×C67C2
socle, prime radicalC24×C67C2×D4
cosocleC22×C4×C67C24
hypercenterC23×Q16D67
hypocenterC67C2×#1971
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×Q16

1574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

1912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 173399);