Finite Group Databasebeta

C42×#11761616 #30854301

order17152
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC42×#11761616

Splittings

SylowC67 ⋊ C42×SD16

Subgroups

subgroupG/H
centerC2×C42C22⋊D67
commutatorC4×C67C22×C42
FrattiniC22×C4C23×D67
FittingC42×D4×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67C23
cosocleC22×C4×C67C24
hypercenterC42×D4D67
hypocenterC67C42×SD16
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×D4

1230 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, 168038);