Finite Group Databasebeta

C8×#14523966 #30746604

order17152
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC8×#14523966

Splittings

SylowC67 ⋊ C8×#103

Subgroups

subgroupG/H
centerC22×C8C22⋊D67
commutatorC4×C67C2×C4×C8
FrattiniC2×C42C22×D67
FittingC8×C4⋊C4×C67C2
socle, prime radicalC23×C67C4×D4
cosocleC2×C42×C67C23
hypercenterC8×C4⋊C4D67
hypocenterC67C8×#103
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C8×C4⋊C4

518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2752 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 60341);