Finite Group Databasebeta

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C3×C5×Dic385 #37528401

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic385

Splittings

derivedC5×C7×C11 ⋊ C3×C4×C5
HallC3×C52×C7×C11 ⋊ C4
HallC52×C7×C11 ⋊ C3×C4
HallC3×C52×C11 ⋊ Dic7
HallC3×C52×C7 ⋊ Dic11
HallC52×C11 ⋊ C3×Dic7
HallC3×C7×C11 ⋊ C5×Dic5
HallC52×C7 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×C5×Dic5
HallC3×C52 ⋊ Dic77
HallC3×C11 ⋊ C5×Dic35
SylowC52 ⋊ C3×Dic77
HallC3×C7 ⋊ C5×Dic55
SylowC11 ⋊ C3×C5×Dic35
SylowC7 ⋊ C3×C5×Dic55

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D385
commutator, hypocenterC5×C7×C11C3×C4×C5
FrattiniC2C3×C5×D385
Fitting, socle, prime radicalC2×C3×C52×C7×C11C2
cosocleC2×C5×C7×C11C2×C3×C5
LCSG ▷ C5×C7×C11
UCSC1 ◁ C2×C3×C5

128 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

5820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 212);