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C5×#13097586 #22547602

order7980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#13097586

Splittings

derived, HallC7×C19 ⋊ C3×C4×C5
HallC5×C19×Dic7 ⋊ C3
HallC5×#87704 ⋊ C4
HallC5×C7×C19 ⋊ C3×C4
HallC19×Dic7 ⋊ C3×C5
Hall#87704 ⋊ C4×C5
HallC5×Dic7 ⋊ C19⋊C3
HallC5×C19 ⋊ ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C4×C19⋊C3
HallDic7 ⋊ C5×C19⋊C3
SylowC19 ⋊ C5×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C4×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#11716325
commutator, hypocenterC7×C19C3×C4×C5
FrattiniC2C5×#11716325
Fitting, socleC2×C5×C7×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

370 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C19⋊C3×ΓL(1,𝔽8)⋊C4, C3×C5×#13097586, C5×C3⋊#13097586
maximal normal subgroup ofC5×C19⋊C3×ΓL(1,𝔽8)⋊C4, C3×C5×#13097586
maximal quotient ofC5×#18012094, C3×C5×#13097586, C5×C3⋊#13097586

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 27);