Finite Group Databasebeta

C2×C4×#14523953 #30853154

order17152
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C24×C42

Aliases

direct productC2×C4×#14523953

Splittings

SylowC67 ⋊ C2×C4×#97

Subgroups

subgroupG/H
centerC22×C42C2×D67
commutatorC2×C67C2×C43
FrattiniC22×C4C23×D67
FittingC22×C4×C8×C67C2
socle, prime radicalC24×C67C22×C4
cosocleC22×C4×C67C24
hypercenterC22×C4×C8D67
hypocenterC67C2×C4×#97
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

4384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 166891);