Finite Group Databasebeta

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C5×Dic5×C112⋊C3 #49137285

order36300
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C11

Aliases

direct productC5×Dic5×C112⋊C3
unambiguous semidirect product(C5×C112×Dic5)⋊C3

Splittings

derivedC5×C112 ⋊ C3×C4×C5
HallC5×C112×Dic5 ⋊ C3
HallC52×C112⋊C3 ⋊ C4
HallC52×C112 ⋊ C3×C4
SylowC112 ⋊ C3×C5×Dic5
SylowC52 ⋊ C4×C112⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5D5×C112⋊C3
commutator, hypocenterC5×C112C3×C4×C5
FrattiniC2C5×D5×C112⋊C3
Fitting, socleC2×C52×C112C2×C3
prime radicalC2×C52×C112⋊C3C2
cosocleC2×C5×C112C2×C3×C5
LCSG ▷ C5×C112
UCSC1 ◁ C2×C5

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

1720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 421);