Finite Group Databasebeta

C2×#22558092 #30745914

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22558092

Splittings

SylowC67 ⋊ C2×#1296

Subgroups

subgroupG/H
centerC24C22⋊Dic67
commutatorC2×C4×C67C2×C42
FrattiniC2×C42C22×D67
FittingC2×#384×C67C2
socle, prime radicalC24×C67C22⋊C4
cosocleC2×C42×C67C23
hypercenterC2×#384D67
hypocenterC67C2×#1296
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#384

878 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, 59651);