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C3×C25×C7⋊Dic7 #28412914

order14700
isoclinismisoclinic class of C7⋊D7
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C7

Aliases

direct productC3×C25×C7⋊Dic7

Splittings

derived, SylowC72 ⋊ C3×C4×C25
HallC3×C72×C25 ⋊ C4
HallC72×C25 ⋊ C3×C4
HallC3×C72 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25C7⋊D7
commutator, hypocenterC72C3×C4×C25
FrattiniC2×C5C3×C5×C7⋊D7
FittingC2×C3×C72×C25C2
socle, prime radicalC2×C3×C5×C72C2×C5
cosocleC2×C5×C72C2×C3×C5
LCSG ▷ C72
UCSC1 ◁ C2×C3×C25

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 93);