Finite Group Databasebeta

C4×#16863951 #31014371

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#16863951

Splittings

FittingC4×C4⋊Q8×C67 ⋊ C2
SylowC67 ⋊ C4×#533

Subgroups

subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC4×C4⋊Q8×C67C2
socle, cosocleC23×C67C25
prime radicalC23×D67C24
hypercenterC4×C4⋊Q8D67
hypocenterC67C4×#533
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C4×C4⋊Q8

2550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 328108);