Finite Group Databasebeta

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C3×C5×C11⋊Dic55 #49137320

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

Aliases

direct productC3×C5×C11⋊Dic55

Splittings

derivedC5×C112 ⋊ C3×C4×C5
HallC3×C52×C112 ⋊ C4
HallC52×C112 ⋊ C3×C4
HallC3×C112 ⋊ C5×Dic5
SylowC112 ⋊ C3×C5×Dic5
HallC3×C52 ⋊ C11⋊Dic11
SylowC52 ⋊ C3×C11⋊Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C5⋊(C11⋊D11)
commutator, hypocenterC5×C112C3×C4×C5
FrattiniC2C3×C5×C5⋊(C11⋊D11)
Fitting, socle, prime radicalC2×C3×C52×C112C2
cosocleC2×C5×C112C2×C3×C5
LCSG ▷ C5×C112
UCSC1 ◁ C2×C3×C5

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7260

Conjugacy classes & character table

9120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 456);