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C2×#13130515 #16796774

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13130515

Splittings

FittingC22×C13×C4⋊C4 ⋊ C4
SylowC13 ⋊ C2×#1733

Subgroups

subgroupG/H
centerC23C2×C22⋊#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×D13D4
cosocleC2×C4×D13C24
hypercenterC22×C4⋊C4#261
hypocenterC13C2×#1733
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

2270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103423);