Finite Group Databasebeta

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C5×#18012158 #37561066

order23940
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×#18012158

Splittings

derived, HallC7×C19 ⋊ C4×C5×C9
HallC5×#11924781 ⋊ C4
HallC5×C7×Dic19 ⋊ C9
Hall#11924781 ⋊ C4×C5
HallC5×C7×C19 ⋊ C4×C9
HallC7×Dic19 ⋊ C5×C9
HallC5×Dic19 ⋊ C7⋊C9
HallC5×C19 ⋊ C4×C7⋊C9
HallDic19 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ #4296⋊C4
SylowC19 ⋊ C4×C5×C7⋊C9
SylowC7 ⋊ C5×#4296⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5#14558808
commutator, hypocenterC7×C19C4×C5×C9
FrattiniC2C5×#14558808
Fitting, socleC2×C5×C7×C19C2×C9
prime radicalC2×C5×C7×C19⋊C3C2×C3
cosocleC2×C7×C19⋊C3C2×C3×C5
LCSG ▷ C7×C19
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2660

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 198);