Finite Group Databasebeta

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C5×C22⋊#4294 #16811840

order3420
automorphism?
homologyAbelianization (H1) = C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC5×C22⋊#4294
unambiguous semidirect productC22⋊(C5×#4294)
unambiguous semidirect product(C22×C5)⋊#4294

Splittings

derived, HallC22×C19 ⋊ C5×C9
HallC22×C5×C19 ⋊ C9
HallC5×C19 ⋊ C22⋊C9
HallC22×C5 ⋊ #4294
SylowC19 ⋊ C5×C22⋊C9
SylowC22 ⋊ C5×#4294

Subgroups

subgroupG/H
center, hypercenterC3×C5C22⋊(C19⋊C3)
commutator, hypocenterC22×C19C5×C9
FrattiniC3C5×C22⋊(C19⋊C3)
Fitting, socle, prime radicalC22×C3×C5×C19C3
cosocleC22×C3×C19C3×C5
LCSG ▷ C22×C19
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 1710

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC25×C22⋊#4294, C52×C22⋊#4294, C5×C22⋊#11924776, …
maximal normal subgroup ofC25×C22⋊#4294, C52×C22⋊#4294, C5×C7×C22⋊#4294, …
maximal quotient ofC25×C22⋊#4294, C52×C22⋊#4294, C5×C22⋊#11924776, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3420, 33);