Finite Group Databasebeta

C4×#16863125 #30746424

order17152
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#16863125

Splittings

FittingC42×C8×C67 ⋊ C2
SylowC67 ⋊ C4×D4⋊C8

Subgroups

subgroupG/H
centerC2×C42D268
commutatorC4×C67C2×C4×C8
FrattiniC2×C42C22×D67
FittingC42×C8×C67C2
socleC23×C67C2×C22⋊C4
prime radicalC22×D268C2×C4
cosocleC2×C42×C67C23
hypercenterC42×C8D67
hypocenterC67C4×D4⋊C8
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×C8

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

4336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 60161);