Finite Group Databasebeta

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C22⋊C4×#11929623 #34447466

order20224
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22⋊C4×#11929623

Splittings

FittingD4×C22⋊C4×C79 ⋊ C2
SylowC79 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingD4×C22⋊C4×C79C2
socle, cosocleC23×C79C25
prime radicalC23×#11929623C2
hypercenterD4×C22⋊C4D79
hypocenterC79C22⋊C4×#41
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ D4×C22⋊C4

5646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

2050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 328765);