Finite Group Databasebeta

C2×#22561351 #30883114

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22561351

Splittings

SylowC67 ⋊ C2×#2024

Subgroups

subgroupG/H
centerC24C2×D268
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC2×#336×C67C2
socle, prime radicalC24×C67C2×D4
hypercenterC2×#336D67
hypocenterC67C2×#2024
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

1518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2704 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 196851);