Finite Group Databasebeta

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C4⋊C4×#13050579 #35422810

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×#13050579

Splittings

FittingC8×C4⋊C4×C83 ⋊ C2
SylowC83 ⋊ C4⋊C4×SD16

Subgroups

subgroupG/H
centerC23C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC8×C4⋊C4×C83C2
socleC23×C83C22×D4
prime radicalC22×D332C23
cosocleC22×C4×C83C24
hypercenterC8×C4⋊C4D83
hypocenterC83C4⋊C4×SD16
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

1030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 187974);