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C7×C3⋊Dic345 #44394455

order28980
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×C3⋊Dic345
unambiguous semidirect productC3⋊(C7×Dic345)
unambiguous semidirect productC23⋊(C7×C3⋊Dic15)

Splittings

derived, HallC32×C5×C23 ⋊ C4×C7
HallC32×C5×C7×C23 ⋊ C4
HallC32×C7×C23 ⋊ Dic5
HallC5×C7×C23 ⋊ C3⋊Dic3
HallC32×C5×C7 ⋊ Dic23
HallC32×C23 ⋊ C7×Dic5
HallC7×C23 ⋊ C3⋊Dic15
HallC5×C23 ⋊ C7×C3⋊Dic3
HallC32×C7 ⋊ Dic115
HallC32×C5 ⋊ C7×Dic23
HallC5×C7 ⋊ C3⋊Dic69
SylowC23 ⋊ C7×C3⋊Dic15
SylowC32 ⋊ C7×Dic115
SylowC5 ⋊ C7×C3⋊Dic69

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊D345
commutator, hypocenterC32×C5×C23C4×C7
FrattiniC2C7×C3⋊D345
Fitting, socle, prime radicalC2×C32×C5×C7×C23C2
cosocleC2×C32×C5×C23C2×C7
LCSG ▷ C32×C5×C23
UCSC1 ◁ C2×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28980

Conjugacy classes & character table

7266 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 124);