Finite Group Databasebeta

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C22⋊C8×Dic134 #30872346

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22⋊C8×Dic134

Splittings

SylowC67 ⋊ Q8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D67
commutatorC22×C67C23×C8
FittingC4×C22⋊C8×C67C2
socleC23×C67C23×C4
prime radicalC24×C67C22×C4
cosocleC22×C4×C67C24
hypercenterC4×C22⋊C8D67
hypocenterC67Q8×C22⋊C8
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C8

1356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 186083);