Finite Group Databasebeta

C2×C4×(C2×D67)⋊C8 #30853343

order17152
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D67)⋊C8

Splittings

FittingC22×C4×C8×C67 ⋊ C2
SylowC67 ⋊ C2×C4×C22⋊C8

Subgroups

subgroupG/H
centerC22×C42C2×D67
commutatorC2×C67C22×C4×C8
FrattiniC22×C4C23×D67
FittingC22×C4×C8×C67C2
socleC24×C67C22×C4
prime radicalC24×D67C2×C4
cosocleC22×C4×C67C24
hypercenterC22×C4×C8D67
hypocenterC67C2×C4×C22⋊C8
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

2414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

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, 167080);