Finite Group Databasebeta

C4×#16863140 #30746771

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#16863140

Splittings

SylowC67 ⋊ C4×#331

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic67
commutatorC2×C4×C67C2×C42
FrattiniC2×C42C22×D67
FittingC4×#127×C67C2
socleC23×C67C2×C22⋊C4
prime radicalC2×#127×C67C22
cosocleC2×C42×C67C23
hypercenterC4×#127D67
hypocenterC67C4×#331
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#127

708 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1924 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 60508);