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C22⋊C4×D556 #31809227

order17792
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22⋊C4×D556

Splittings

FittingC4×C22⋊C4×C139 ⋊ C2
SylowC139 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D139
commutatorC22×C139C23×C4
FittingC4×C22⋊C4×C139C2
socle, cosocleC23×C139C24
prime radicalC23×D556C2
hypercenterC4×C22⋊C4D139
hypocenterC139D4×C22⋊C4
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ C4×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4448

Conjugacy classes & character table

2810 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17792, 7333);