Finite Group Databasebeta

← Prev (#30747012) Next (#30747014) →

C4×#16863146 #30747013

order17152
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#16863146

Splittings

SylowC67 ⋊ C4×#334

Subgroups

subgroupG/H
centerC2×C42C22⋊D67
commutatorC4×C67C2×C4×C8
FrattiniC2×C42C22×D67
FittingC4×C4⋊C8×C67C2
socle, prime radicalC23×C67C2×C4⋊C4
cosocleC2×C42×C67C23
hypercenterC4×C4⋊C8D67
hypocenterC67C4×#334
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C43 ◁ C4×C4⋊C8

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

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, 60750);