Finite Group Databasebeta

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C7×#4294⋊Dic5 #37560905

order23940
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×#4294⋊Dic5
unambiguous semidirect product#4294⋊(C7×Dic5)

Splittings

derived, HallC5×C19 ⋊ C4×C7×C9
HallC5×C7×#4294 ⋊ C4
HallC7×Dic95 ⋊ C9
HallC7×#4294 ⋊ Dic5
HallC5×#4294 ⋊ C4×C7
HallC5×C7×C19 ⋊ C4×C9
HallDic95 ⋊ C7×C9
Hall#4294 ⋊ C7×Dic5
HallC7×C19 ⋊ C9×Dic5
HallC5×C7 ⋊ #4294⋊C4
SylowC19 ⋊ C7×C9×Dic5
SylowC5 ⋊ C7×#4294⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C5⋊(D19⋊C3)
commutator, hypocenterC5×C19C4×C7×C9
FrattiniC2×C3C7×C5⋊(D19⋊C3)
Fitting, socle, prime radicalC2×C3×C5×C7×C19C2×C3
cosocleC2×C3×C5×C19C2×C3×C7
LCSG ▷ C5×C19
UCSC1 ◁ C2×C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23940

Conjugacy classes & character table

1134 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 37);