Finite Group Databasebeta

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C4×C16×D127 #30640315

order16256
isoclinismisoclinic class of D127
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C16×D127

Splittings

FittingC4×C16×C127 ⋊ C2
derived, SylowC127 ⋊ C2×C4×C16

Subgroups

subgroupG/H
center, hypercenterC4×C16D127
commutator, hypocenterC127C2×C4×C16
FrattiniC2×C8C22×D127
FittingC4×C16×C127C2
socleC22×C127C22×C8
prime radicalC22×D127C2×C8
cosocleC2×C8×C127C23
LCSG ▷ C127
UCSC1 ◁ C4×C16

216 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 137 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

4160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 6095);