Finite Group Databasebeta

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C2×#22558698 #30822923

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22558698

Splittings

FittingC2×C4×C22⋊C4×C67 ⋊ C2
SylowC67 ⋊ C2×#1501

Subgroups

subgroupG/H
centerC22×C4(C2×D67)⋊C4
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC2×C4×C22⋊C4×C67C2
socleC23×C67C2×C22⋊C4
prime radicalC2×#16863907C2
cosocleC22×C4×C67C24
hypercenterC2×C4×C22⋊C4D67
hypocenterC67C2×#1501
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 136660);