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C23×C3⋊Dic105 #44394454

order28980
automorphism?
homologyAbelianization (H1) = C4×C23 · Schur multiplier (H2) = C3

Aliases

direct productC23×C3⋊Dic105
unambiguous semidirect productC3⋊(C23×Dic105)
unambiguous semidirect productC7⋊(C23×C3⋊Dic15)

Splittings

derived, HallC32×C5×C7 ⋊ C4×C23
HallC32×C5×C7×C23 ⋊ C4
HallC32×C7×C23 ⋊ Dic5
HallC32×C5×C23 ⋊ Dic7
HallC5×C7×C23 ⋊ C3⋊Dic3
HallC32×C23 ⋊ Dic35
HallC7×C23 ⋊ C3⋊Dic15
HallC5×C23 ⋊ C3⋊Dic21
HallC32×C7 ⋊ Dic5×C23
HallC32×C5 ⋊ C23×Dic7
HallC5×C7 ⋊ C23×C3⋊Dic3
SylowC32 ⋊ C23×Dic35
SylowC7 ⋊ C23×C3⋊Dic15
SylowC5 ⋊ C23×C3⋊Dic21

Subgroups

subgroupG/H
center, hypercenterC2×C23C3⋊D105
commutator, hypocenterC32×C5×C7C4×C23
FrattiniC2C23×C3⋊D105
Fitting, socle, prime radicalC2×C32×C5×C7×C23C2
cosocleC2×C32×C5×C7C2×C23
LCSG ▷ C32×C5×C7
UCSC1 ◁ C2×C23

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28980

Conjugacy classes & character table

7314 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 123);