Finite Group Databasebeta

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C5×#13089712⋊C5 #49137218

order36300
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×#13089712⋊C5
unambiguous semidirect product#13089712⋊C52
unambiguous semidirect product(C5×#13089712)⋊C5

Splittings

derived, HallC112⋊C3 ⋊ C4×C52
HallC5×(C112⋊C3)⋊C5 ⋊ C4
HallC5×#10597243 ⋊ Dic3
Hall#13089712 ⋊ C52
SylowC112 ⋊ C52×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C5#10624391⋊C5
commutator, hypocenterC112⋊C3C4×C52
FrattiniC2C5×#10624391⋊C5
Fitting, socleC2×C5×C112C5×D3
prime radicalC2×C5×(C112⋊C3)⋊C5C2
cosocleC2×C112⋊C3C2×C52
LCSG ▷ C112⋊C3
UCSC1 ◁ C2×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 354);