Finite Group Databasebeta

C22×#16863123 #30822172

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#16863123

Splittings

FittingC22×C4⋊C8×C67 ⋊ C2
SylowC67 ⋊ C22×D4⋊C8

Subgroups

subgroupG/H
centerC23×C4C22⋊D67
commutatorC4×C67C23×C8
FrattiniC42C23×D67
FittingC22×C4⋊C8×C67C2
socleC24×C67C22⋊C4
prime radicalC23×D268C4
cosocleC42×C67C24
hypercenterC22×C4⋊C8D67
hypocenterC67C22×D4⋊C8
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4⋊C8

1886 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, 135909);