Finite Group Databasebeta

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C2×C5×#1088 #11761978

order1080
isoclinismisoclinic class of #1088
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×#1088

Splittings

FittingC2×C5×H(3,𝔽3) ⋊ C4
derived, SylowH(3,𝔽3) ⋊ C2×C4×C5
HallC5×H(3,𝔽3) ⋊ C2×C4

Subgroups

subgroupG/H
center, socle, hypercenterC2×C3×C5#157
commutator, hypocenterH(3,𝔽3)C2×C4×C5
FrattiniC3C2×C5×#157
FittingC2×C5×H(3,𝔽3)C4
prime radicalC2×C5×#272C2
cosocle#272C22×C5
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C2×C3×C5

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 324);