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C7×C3⋊(Dic61⋊C3) #29506784

order15372
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(Dic61⋊C3)
unambiguous semidirect productC3⋊(C7×Dic61⋊C3)
unambiguous semidirect productDic183⋊(C3×C7)

Splittings

derivedC3×C61 ⋊ C3×C4×C7
HallC3×C7×C61⋊C3 ⋊ C4
HallC3×C61⋊C3 ⋊ C4×C7
HallC7×C61 ⋊ C3×Dic3
SylowC61 ⋊ C3×C7×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(D61⋊C3)
commutator, hypocenterC3×C61C3×C4×C7
FrattiniC2C7×C3⋊(D61⋊C3)
Fitting, socleC2×C3×C7×C61C2×C3
prime radicalC2×C3×C7×C61⋊C3C2
cosocleC2×C3×C61C2×C3×C7
LCSG ▷ C3×C61
UCSC1 ◁ C2×C7

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5124

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15372, 94);