Finite Group Databasebeta

C4×#16863273 #30776983

order17152
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productC4×#16863273

Splittings

FittingC2×C4×C22⋊C4×C67 ⋊ C2
SylowC67 ⋊ C4×#386

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutatorC22×C67C22×C42
FrattiniC24C23×D67
FittingC2×C4×C22⋊C4×C67C2
socle, cosocleC24×C67C24
prime radicalC23×C22⋊D67C22
hypercenterC2×C4×C22⋊C4D67
hypocenterC67C4×#386
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2752 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 90720);