Finite Group Databasebeta

C4×#16863135 #30746746

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#16863135

Splittings

FittingC4×#97×C67 ⋊ C2
SylowC67 ⋊ C4×#329

Subgroups

subgroupG/H
centerC22×C4(C2×D67)⋊C4
commutatorC2×C4×C67C2×C42
FrattiniC2×C42C22×D67
FittingC4×#97×C67C2
socleC23×C67C2×C22⋊C4
prime radicalC22×D268C2×C4
cosocleC2×C42×C67C23
hypercenterC4×#97D67
hypocenterC67C4×#329
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#97

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 60483);