Finite Group Databasebeta

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C4⋊C4×C22⋊D109 #28365931

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×C22⋊D109

Splittings

FittingC22×C4⋊C4×C109 ⋊ C2
SylowC109 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
FittingC22×C4⋊C4×C109C2
socle, cosocleC23×C109C24
prime radicalC22×C22⋊D109C22
hypercenterC22×C4⋊C4D109
hypocenterC109D4×C4⋊C4
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C22×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 7409);