Finite Group Databasebeta

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C2×C3×C25×D93 #42124464

order27900
isoclinismisoclinic class of D93
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C25×D93
unambiguous semidirect product(C2×C3)⋊(C3×C25×D31)

Splittings

FittingC2×C32×C25×C31 ⋊ C2
derivedC3×C31 ⋊ C22×C3×C25
HallC32×C25×C31 ⋊ C22
HallC25×C31 ⋊ C2×C3×D3
HallC32×C31 ⋊ C22×C25
HallC32×C25 ⋊ C2×D31
SylowC31 ⋊ C2×C3×D3×C25
SylowC32 ⋊ C2×C25×D31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25D93
commutator, hypocenterC3×C31C22×C3×C25
FrattiniC5C2×C3×C5×D93
FittingC2×C32×C25×C31C2
socleC2×C32×C5×C31C2×C5
prime radicalC2×C3×C5×D93C5
cosocleC3×C5×C31C22×C3×C5
LCSG ▷ C3×C31
UCSC1 ◁ C2×C3×C25

132 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

7200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 211);