Finite Group Databasebeta

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C3×C5×Dic95 #19152803

order5700
isoclinismisoclinic class of D95
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic95

Splittings

derivedC5×C19 ⋊ C3×C4×C5
HallC3×C52×C19 ⋊ C4
HallC52×C19 ⋊ C3×C4
HallC3×C52 ⋊ Dic19
HallC3×C19 ⋊ C5×Dic5
SylowC52 ⋊ C3×Dic19
SylowC19 ⋊ C3×C5×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D95
commutator, hypocenterC5×C19C3×C4×C5
FrattiniC2C3×C5×D95
Fitting, socleC2×C3×C52×C19C2
LCSG ▷ C5×C19
UCSC1 ◁ C2×C3×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1470 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×#4294⋊Dic5, C5×C9×Dic95, C3×C5×(C19⋊C3)⋊Dic5, …
maximal normal subgroup ofC5×#4294⋊Dic5, C5×C9×Dic95, C3×C5×(C19⋊C3)⋊Dic5, …
maximal quotient ofC5×C9×Dic95, C32×C5×Dic95, C3×C5×Dic285

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 60);