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Dic15×C71⋊C7 #44447139

order29820
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productDic15×C71⋊C7
unambiguous semidirect productC3⋊(Dic5×C71⋊C7)
unambiguous semidirect product(Dic15×C71)⋊C7

Splittings

derived, HallC3×C5×C71 ⋊ C4×C7
HallC3×C5×C71⋊C7 ⋊ C4
HallDic15×C71 ⋊ C7
HallC5×C71⋊C7 ⋊ Dic3
HallC3×C71⋊C7 ⋊ Dic5
HallC5×C71 ⋊ C7×Dic3
HallC3×C71 ⋊ C7×Dic5
SylowC71 ⋊ C7×Dic15
HallC3×C5 ⋊ C4×C71⋊C7
SylowC5 ⋊ Dic3×C71⋊C7
SylowC3 ⋊ Dic5×C71⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D15×C71⋊C7
commutator, hypocenterC3×C5×C71C4×C7
Fitting, socle, cosocleC2×C3×C5×C71C2×C7
prime radicalC2×C3×C5×C71⋊C7C2
LCSG ▷ C3×C5×C71
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4260

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 27);