Finite Group Databasebeta

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C2×#23761889 #34255361

order20224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#23761889

Splittings

FittingC2×C4×C22⋊C4×C79 ⋊ C2
SylowC79 ⋊ C2×#1501

Subgroups

subgroupG/H
centerC22×C4(C2×D79)⋊C4
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC2×C4×C22⋊C4×C79C2
socleC23×C79C2×C22⋊C4
prime radicalC2×#19099074C2
cosocleC22×C4×C79C24
hypercenterC2×C4×C22⋊C4D79
hypocenterC79C2×#1501
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

3196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 136660);